Optimal Recovery of Missing Values for Non-Negative Matrix Factorization

Additive Non-negative Matrix Factorization for Missing Data

Non-negative matrix factorization (NMF) has previously been shown to be a useful decomposition for multivariate data. We interpret the factorization in a new way and use it to generate missing attributes from test data. We provide a joint optimization scheme for the missing attributes as well as the NMF factors. We prove the monotonic convergence of our algorithms. We present classification res...

Computational auditory induction by missing-data non-negative matrix factorization

The human auditory system has the ability, known as auditory induction, to estimate the missing parts of a continuous auditory stream briefly covered by noise and perceptually resynthesize them. Humans are thus able to simultaneously analyze an auditory scene and reconstruct the underlying signal. In this article, we formulate this ability as a non-negative matrix factorization (NMF) problem wi...

Boolean Matrix Factorization with missing values

Is it possible to meaningfully analyze the structure of a Boolean matrix for which 99% data is missing? Real-life data sets usually contain a high percentage of missing values which hamper structure estimation from the data and the difficulty only increases when the missing values dominate the known elements in the data set. There are good real-valued factorization methods for such scenarios, b...

Iterative Weighted Non-smooth Non-negative Matrix Factorization for Face Recognition

Non-negative Matrix Factorization (NMF) is a part-based image representation method. It comes from the intuitive idea that entire face image can be constructed by combining several parts. In this paper, we propose a framework for face recognition by finding localized, part-based representations, denoted “Iterative weighted non-smooth non-negative matrix factorization” (IWNS-NMF). A new cost fun...

Non-negative matrix factorization